Lattice and Electronic properties of VO$_2$ with the SCAN(+$U$) approach

Appropriate consideration of the electron correlation is essential to reproduce the intriguing metal-insulator transition accompanying the Peierls-type structural transition in VO$_2$. In the density functional theory-based approach, this depends on the choice of the exchange-correlation functional. Here, using a newly developed strongly constrained and appropriately norm (SCAN) functional, we investigate the lattice and electronic properties of the metallic rutile phase of VO$_2$ ($R$-VO$_2$) from the first-principles calculations. We also explored the role of the Coulomb correlation $U$. By adding $U$, we found that the phonon instability properly describes the Peierls-type distortions. The orbital-decomposed density of states presents the orbital selective behavior with the SCAN+$U$, which is susceptible to the one-dimensional Peierls distortion. Our results suggest that even with the SCAN functional, the explicit inclusion of the Coulomb interaction is necessary to describe the structural transition of VO$_2$.